Question

The magic carpet charges $90 for installation and $9 per square yard of carpeting. The carpeterias installation price is $50 but the store charges $13 for each square yard. For what number of square yards if carpeting will the cost,including installation, be the same for both stores?

Answer 1

For this case, the first thing we must do is define variables.

We have then:

x: number of square yards of carpeting.

y: total cost.

We now write the equation for each store.

We have then:

For The magic carpet:

$y = 9x + 90$

For The carpeterias:

$y = 13x + 50$

By the time the price is the same we have:

$13x + 50 = 9x + 90$

From here, we clear the value of x.

We have then:

$13x-9x = 90-50$

$4x = 40$

$x = \frac{40}{4}$

$x = 10$

Answer:

For 10 square yards the cost is the same in both stores.